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| Synopsis |
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| class C a where | | | | subtract :: C a => a -> a -> a | | | sum :: C a => [a] -> a | | | sum1 :: C a => [a] -> a | | | elementAdd :: C x => (v -> x) -> T (v, v) x | | | elementSub :: C x => (v -> x) -> T (v, v) x | | | elementNeg :: C x => (v -> x) -> T v x | | | (<*>.+) :: C x => T (v, v) (x -> a) -> (v -> x) -> T (v, v) a | | | (<*>.-) :: C x => T (v, v) (x -> a) -> (v -> x) -> T (v, v) a | | | (<*>.-$) :: C x => T v (x -> a) -> (v -> x) -> T v a | | | propAssociative :: (Eq a, C a) => a -> a -> a -> Bool | | | propCommutative :: (Eq a, C a) => a -> a -> Bool | | | propIdentity :: (Eq a, C a) => a -> Bool | | | propInverse :: (Eq a, C a) => a -> Bool |
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| Class
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Additive a encapsulates the notion of a commutative group, specified
by the following laws:
a + b === b + a
(a + b) + c === a + (b + c)
zero + a === a
a + negate a === 0
Typical examples include integers, dollars, and vectors.
Minimal definition: +, zero, and (negate or '(-)')
| | | Methods | | | zero element of the vector space
| | | | add and subtract elements
| | | | | | inverse with respect to +
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| |  Instances | | C Double | | C Float | | C Int | | C Int8 | | C Int16 | | C Int32 | | C Int64 | | C Integer | | C Word | | C Word8 | | C Word16 | | C Word32 | | C Word64 | | C T | | C T | | C T | | C v => C ([] v) | | Integral a => C (Ratio a) | | (Ord a, C a) => C (T a) | | C a => C (T a) | | C a => C (T a) | | (C a, C a, C a) => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | (C a, C a) => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | (Eq a, C a) => C (T a) | | (Eq a, C a) => C (T a) | | C a => C (T a) | | C v => C (b -> v) | | (C v0, C v1) => C ((,) v0 v1) | | (Ord i, Eq v, C v) => C (Map i v) | | (Ord a, C b) => C (T a b) | | (C u, C a) => C (T u a) | | C v => C (T a v) | | (Ord i, C a) => C (T i a) | | C v => C (T a v) | | (C v0, C v1, C v2) => C ((,,) v0 v1 v2) |
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| subtract :: C a => a -> a -> a | Source |
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| subtract is (-) with swapped operand order.
This is the operand order which will be needed in most cases
of partial application.
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| Complex functions
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| Sum up all elements of a list.
An empty list yields zero.
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| Sum up all elements of a non-empty list.
This avoids including a zero which is useful for types
where no universal zero is available.
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| Instance definition helpers
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| elementAdd :: C x => (v -> x) -> T (v, v) x | Source |
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| Instead of baking the add operation into the element function,
we could use higher rank types
and pass a generic uncurry (+) to the run function.
We do not do so in order to stay Haskell 98
at least for parts of NumericPrelude.
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| elementSub :: C x => (v -> x) -> T (v, v) x | Source |
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| elementNeg :: C x => (v -> x) -> T v x | Source |
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| (<*>.+) :: C x => T (v, v) (x -> a) -> (v -> x) -> T (v, v) a | Source |
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addPair :: (Additive.C a, Additive.C b) => (a,b) -> (a,b) -> (a,b)
addPair = Elem.run2 $ Elem.with (,) <*>.+ fst <*>.+ snd
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| (<*>.-) :: C x => T (v, v) (x -> a) -> (v -> x) -> T (v, v) a | Source |
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| (<*>.-$) :: C x => T v (x -> a) -> (v -> x) -> T v a | Source |
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| Instances for atomic types
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| Produced by Haddock version 2.4.2 |
